An Introduction to Optimal Designs for Social and Biomedical ResearchPDF|Epub|txt|kindle电子书版本网盘下载

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1 Introduction to designs1

1.1 Introduction1

1.2 Stages of the research process4

1.2.1 Choice of a ‘good’ design5

1.3 Research design6

1.3.1 Choice of independent variables and levels6

1.3.2 Units of analysis6

1.3.3 Variables7

1.3.4 Replication8

1.4 Types of research designs8

1.5 Requirements for a ‘good’ design9

1.5.1 Statistical conclusion validity10

1.5.2 Internal validity12

1.5.3 Control of（unwanted）variation13

1.6 Ethical aspects of design choice16

1.7 Exact versus approximate designs17

1.8 Examples19

1.8.1 Radiation dosage example19

1.8.2 Designs for the Poggendorff and Ponzo illusion experiments20

1.8.3 Uncertainty about best fitting regression models22

1.8.4 Designs for a priori contrasts among composite faces23

1.8.5 Designs for calibration of item parameters in item response theory models24

1.9 Summary26

2 Designs for simple linear regression27

2.1 Design problem for a linear model27

2.1.1 The design28

2.1.2 The linear regression model31

2.1.3 Estimation of parameters and efficiency32

2.2 Designs for radiation-dosage example35

2.3 Relative efficiency and sample size36

2.4 Simultaneous inference37

2.5 Optimality criteria39

2.5.1 D-optimality criterion40

2.5.2 A-optimality criterion41

2.5.3 G-optimality criterion41

2.5.4 E-optimality criterion43

2.5.5 Number of distinct design points43

2.6 Relative efficiency44

2.7 Matrix formulation of designs for linear regression44

2.8 Summary49

3 Designs for multiple linear regression analysis51

3.1 Design problem for multiple linear regression51

3.1.1 The design52

3.1.2 The multiple linear regression model54

3.1.3 Estimation of parameters and efficiency54

3.2 Designs for vocabulary-growth study56

3.3 Relative efficiency and sample size60

3.4 Simultaneous inference61

3.5 Optimality criteria for a subset of parameters62

3.6 Relative efficiency64

3.7 Designs for polynomial regression model65

3.7.1 Exact D-optimal designs for a quadratic regression model69

3.7.2 Scale dependency of A-and E-optimality criteria71

3.8 The Poggendorff and Ponzo illusion study71

3.9 Uncertainty about best fitting regression models76

3.10 Matrix notation of designs for multiple regression models79

3.10.1 Design for regression models with two independent vari-ables80

3.10.2 Design for regression models with two non-additive inde-pendent variables82

3.11 Summary85

4 Designs for analysis of variance models87

4.1 A typical design problem for an analysis of variance model87

4.1.1 The design89

4.1.2 The analysis of variance model90

4.1.3 Formulation of an ANOVA model as a regression model91

4.2 Estimation of parameters and efficiency95

4.2.1 Measures of uncertainty96

4.3 Simultaneous inference and optimality criteria97

4.4 Designs for groups under stress study98

4.4.1 A priori planned unequal sample sizes99

4.4.2 Not planned unequal sample sizes100

4.5 Specific hypotheses and contrasts101

4.5.1 Loss of efficiency and power103

4.6 Designs for the composite faces study106

4.7 Balanced designs versus unbalanced designs109

4.8 Matrix notation for Groups under Stress study109

4.9 Summary111

5 Designs for logistic regression models113

5.1 Design problem for logistic regression113

5.2 The design114

5.3 The logistic regression model115

5.3.1 Design for a single dichotomous independent variable116

5.3.2 Design for multiple qualitative independent variables122

5.3.3 Design for a single quantitative independent variable125

5.3.4 Design for two independent quantitative variables130

5.4 Approaches to deal with local optimality133

5.5 Designs for calibration of item parameters in item response theory models134

5.6 Matrix formulation of designs for logistic regression137

5.6.1 Hours of practice experiment138

5.6.2 Problem solving study140

5.7 Summary141

6 Designs for multilevel models143

6.1 Design problem for multilevel models143

6.1.1 The design144

6.1.2 Validity considerations146

6.2 The multilevel regression model147

6.2.1 Cluster randomization of treatment147

6.2.2 Subject randomization of treatment149

6.3 Cluster versus subject randomization151

6.4 Cost function153

6.5 Example：Nursing home study155

6.5.1 Cluster randomization157

6.5.2 Subject randomization159

6.6 Optimal design and power160

6.6.1 Power for cluster randomized design162

6.6.2 Power for multi-center design164

6.6.3 Increase of efficiency and power by including covariates165

6.6.4 Unequal sample sizes165

6.7 Design effect in multilevel surveys166

6.7.1 Values of intra-class correlation ρ168

6.7.2 Cluster randomized sampling versus simple random sam-pling168

6.8 Matrix formulation of the multilevel model169

6.8.1 Cluster randomization of treatment170

6.8.2 Subject randomization of treatment172

6.9 Summary174

7 Longitudinal designs for repeated measurement models175

7.1 Design problem for repeated measurements175

7.2 The design179

7.3 Analysis techniques for repeated measures180

7.4 The linear mixed effects model for repeated measurement data181

7.4.1 Random intercept model182

7.4.2 Random intercept and slope model183

7.5 Variance-covariance structures184

7.5.1 Compound symmetry structure184

7.5.2 Auto-correlation structure185

7.6 Estimation of parameters and efficiency187

7.6.1 Small sample behaviour of estimators188

7.7 Bone mineral density example189

7.7.1 Improvement of the longitudinal design194

7.8 Cost function196

7.9 D-optimal designs for linear mixed effects models with auto-correlated errors200

7.10 Miscellanea207

7.10.1 Homoscedasticity207

7.10.2 Uninformative dropout208

7.11 Matrix formulation of the linear mixed effects model208

7.12 Summary211

8 Two-treatment crossover designs213

8.1 Design problem for crossover studies213

8.2 The design216

8.3 Confounding treatment effects with nuisance effects218

8.4 The linear model for crossover designs221

8.5 Estimation of parameters and efficiency223

8.6 Cost and efficiency of the crossover design223

8.6.1 Cost function226

8.7 Optimal crossover designs for two treatments229

8.7.1 Some further observations231

8.8 Matrix formulation of the mixed model for crossover designs232

8.9 Summary235

9 Alternative optimal designs for linear models237

9.1 Introduction237

9.2 Information matrix238

9.3 DA-or Ds-optimal designs239

9.4 Extrapolation optimal design241

9.5 L-optimal designs242

9.6 Bayesian optimal designs244

9.7 Minimax optimal design247

9.8 Multiple-objective optimal designs250

9.8.1 Constrained optimal design251

9.8.2 Compound optimal design253

9.9 Summary255

10 Optimal designs for nonlinear models257

10.1 Introduction257

10.2 Linear models versus nonlinear models258

10.2.1 The Arrhenius equation258

10.2.2 The compartmental model259

10.2.3 The Michaelis-Menten model260

10.2.4 The Emax model261

10.3 Design issues for nonlinear models261

10.3.1 Local optimality262

10.4 Alternative optimal designs with examples265

10.4.1 DA or Ds-optimal design265

10.4.2 Extrapolation optimal design266

10.4.3 Optimal design for estimating percentiles266

10.5 Bayesian optimal designs267

10.6 Minimax optimal design269

10.7 Multiple-objective optimal designs271

10.8 Optimal design for model discrimination273

10.9 Summary275

11 Resources for the construction of optimal designs277

11.1 Introduction277

11.2 Sequential construction of optimal designs278

11.3 Exchange of design points283

11.3.1 Exchange algorithms283

11.4 Other algorithms284

11.5 Optimal design software285

11.6 A web site for finding optimal designs286

11.6.1 Optimal designs for the Michaelis-Menten and Emax models288

11.6.2 Optimal designs for discriminating among toxicological models290

11.7 Summary294

References295

Author Index313

Subject Index319